Modeling, Analysis, and Design of Multi-tier and Cognitive Cellular Wireless Networks - Prof Ekram...

Modeling, Analysis, and Design of Multi-tier and Cognitive Cellular Wireless Networks

Modeling, Analysis, and Design of Multi-tier andCognitive Cellular Wireless Networks

Ekram Hossain

Department of Electrical and Computer EngineeringUniversity of Manitoba, Winnipeg, Canada

http://home.cc.umanitoba.ca/∼hossaina

Institut Technology Telcom (IT Telkom)27 August 2013

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“Wireless Communications, Networks, and ServicesResearch Group” at U. of Manitoba

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“Wireless Communications, Networks, and ServicesResearch Group” at U. of Manitoba

Current research interests:

Cognitive radio and dynamic spectrum access

Hierarchical cellular wireless networks (small cell networks)

Green cellular radio systems

Applied game theory and network economics

Current group members:

3 PDF, 8 Ph.D. students, 2 M.Sc. students

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Outline

1 Introduction

2 Challenges in Modeling, Analysis, and Design of HetNets

3 Preliminaries: Stochastic Geometry and Poisson Point Process

4 Categorization of Performance Evaluation Techniques

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Introduction

Evolution of the population of wireless devices

Nu

mb

er o

f co

nn

ecte

d d

evic

es

2020

10b

20b

30b

40b

50b

2015 2010

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Introduction

Evolution of the population of wireless devices

Global Mobile Data Traffic Forecast Report presented byCisco predicts 2.4 exabytes mobile data traffic per month forthe year 2013.

M2M communications and IoT (Internet of Things)

Three evolution phases of user population:1 connected consumer electronics phase (smart phones, tablets,

computers, IPTVs)2 connected industry phase (sensor networks, industry and

buildings automation, surveillance, and eHealth applications)3 connected everything phase (IoT phase)

A significant part of this traffic will be carried through cellularnetworks.

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Introduction

Multi-tier cellular wireless networks

Improvement of cell coverage, network capacity, and betterquality-of-service (QoS) provisioning are some of the majorchallenges for next generation cellular networks.

Universal frequency reuse and make transmitters and receiverscloser

Hierarchical layering of cells (referred to as HetNets), anefficient solution to improve cell coverage and networkcapacity.

Adopted in the evolving Long Term Evolution(LTE)/LTE-Advanced (LTE-A) systems

3GPP Release-8 (LTE), 3GPP Release 10 onwards(LTE-Advanced)

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Introduction

LTE/LTE-A HetNet

Long-Term Evolution (LTE) and LTE-Advanced systems aredesigned to support high-speed packet-switched services in 4Gcellular wireless networks.

The cells or radio base stations in LTE/LTE-A can beclassified as: i) macrocell base station (referred as MeNB),and ii) small cells (e.g., microcells, picocells, femtocells).

“Small cell” is an umbrella term for low-power radio accessnodes that operate in both licensed and unlicensed spectrumand have a range of 10 meter to several hundred meters.

Small cells will improve the cell coverage and areaspectral-efficiency (capacity per unit area).

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Introduction

LTE/LTE-A HetNet

Macrocell Base Station A (MeNB-A)

MeNB-A UE 1

HeNB-A1 UE 1MeNB-A UE 2

Picocell

PC-A1RN-A1 UE 1

Relay Node

RN-A1

MeNB-A UE 3

PC-A1 UE 1

PC-A1 UE 2

HeNB-A1

HeNB-A2 UE 1HeNB-A2

HeNB-A3 UE 1 HeNB-A3

X2Un

MeNB-B

HeNB-B1 UE 1

MeNB-B UE 2

PC-B1

RN-B1 UE 1

Relay Node

RN-B1

MeNB-B UE 1

PC-B1 UE 1

PC-B1 UE 2

HeNB-B1

HeNB-B2 UE 1

HeNB-B2

X2

Un

MeNB-C

MeNB-C UE 1

HeNB-C3 UE 1

MeNB-C UE 2

MeNB-C UE 3

RN-C1 UE 1

Relay Node

RN-C1

MeNB-C UE 4

HeNB-C3 HeNB-C2 UE 1

HeNB-C2

HeNB-C1 UE 1

HeNB-C1

X2

UnPicocell

PC-C1PC-C1 UE 1

PC-C1 UE 2

LTE Evolved Packet Core

HeNB Gateway

MME / S-GW

HeNB Gateway

X2

X2

X2

S1

S1

S1

S1 S1

S1

Internet

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Introduction

Comparison among different radio base stations inLTE/LTE-A

Attributes MeNB Picocell HeNB Wi-Fi

BS Installation Mobile Operator Mobile Operator Customer Customer

Site Acquisition

Mobile Operator Mobile Operator Customer Customer

Transmission Range

300-2000 m 40-100 m 10-30 m 100-200 m

Transmission Power

40 W (approx.) 200 mW- 2 W 10-100 mW 100-200 mW

Band License Licensed band Licensed band Licensed band Unlicensed band

System Bandwidth

5, 10, 15, 20 MHz (with CA up to 100 MHz)



5, 10, 20 MHz

Transmission Rate

up to 1 Gbps up to 300 Mbps 100 Mbps-1 Gbps

up to 600 Mbps

Cost $ 60,000/yr $ 10,000/yr $ 200/yr $ 100-200/yr

Power Consumption

High Moderate Low Low

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Introduction

Motivations for small cells

High data rate and improved quality-of-services to subscribers

Eliminate coverage holes in macrocell footprint

Extended battery life of mobile phones

Macrocell load reduced (hence more resources for macrocellusers)

Mitigate spectrum underutilization problem

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Challenges in Modeling, Analysis, and Design of HetNets

HetNet characteristics

Introduction of small cells results in a substantial shift in thecellular network architecture with features such as

topological randomnesshigh variability in the specifications of the network elementsunbalanced uplink-downlink associationtraffic offloading and load balancingvery dense deployment

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Topological randomness

!

5

(a) (b) (c)

Fig. 2: Example of different macrocell only models. Traditional grid networks remain the most popular, but 4G systems havesmaller and more irregular cell sizes, and perhaps are just as well modeled by a totally random BS placement.

to the femtocell user is assumed to be only from the variousmacrocells, which in a fairly sparse femtocell deployment, isprobably accurate. In the uplink as well, the strong interferenceis bound to come from nearby mobiles transmitting at highpower up to the macro base station, so the model may bereasonable. The main limitation of this model vs. Model 1 isthat the performance of downlink macrocell users – who mayexperience strong femtocell interference depending on theirposition – cannot be accurately characterized.

The third model, which appears to be the most recent, isto allow both the macrocells and femtocells to be randomlyplaced. This is the approach of three papers in this specialissue [61]–[63], and to the best of our knowledge, theseare the first full-length works to propose such an approach(earlier versions being [64], [65]. Both of these papers arefor the downlink only and an extension to the uplink wouldbe desirable. An appealing aspect of this approach is that therandomness actually allows significantly improved tractabilityand the SINR distribution can be found explicitly. This mayallow the fundamental impact of different PHY and MACdesigns to be evaluated theoretically in the future.

A fourth model is simply to keep all the channel gains(including interfering channels) and possibly even the variousper-user capacities general, without specifying the precisespatial model for the various base stations, e.g. [66], [67]. Thiscan be used in many higher-level formulations, e.g. for gametheory [59], power control, and resource allocation, althoughultimately some distribution of these channel gains must beassumed in order to do any simulation, and the gains areto a first order determined by the locations of the varioustransmitting sources. So ultimately, this fourth model typicallywill conform to one of the above three models.

V. OVERVIEW OF KEY CHALLENGES

Building on the models developed in last section, as well asthe preceding discussions on standards and historical trends,

in this section we turn our attention to some of the newchallenges that arise in femtocell deployments. To motivatefuture research and an appreciation for the disruptive potentialof femtocells, we now overview the broader challenges of fem-tocells, focusing on both technical and economic/regulatoryissues.

A. Technical Challenges

1) Interference Coordination: Perhaps the most significantand widely-discussed challenge for femtocell deployments isthe possibility of stronger, less predictable, and more variedinterference, as shown in Fig 3. This occurs predominantlywhen femtocells are deployed in the same spectrum as thelegacy (outdoor) wireless network, but can also occur evenwhen femtocells are in a different but adjacent frequency banddue to out-of-band radiation, particularly in dense deploy-ments. As discussed in the previous section, the introductionof femtocells fundamentally alters the cellular topology bycreating an underlay of small cells, with largely randomplacements and possible restrictions on access to certain BSs.Precise characterizations of the interference conditions in suchheterogeneous and multi-tier networks has been the subject ofextensive study [68], [69]. One of the important and perhapssurprising results shown in [61] is that in principle, with open-access and strongest cell selection, heterogeneous, multi-tierdeployments do not worsen the overall interference conditionsor even change the SINR statistics. This “invariance prop-erty” has also been observed in real-world systems by NokiaSiemens [70] and Qualcomm [71], and provides optimism thatfemtocell deployments need not compromise the integrity ofthe existing macrocell network.

However, in practice, at least two aspects of femtocellnetworks can degrade the interference significantly. First,under closed access, unregistered mobiles cannot connect toa femtocell even if they are close by. As noted in Section

J. G. Andrews, H. Claussen, M. Dohler, S. Rangan, and M. C. Reed, “Femtocells: Past, present, and future,” IEEEJournal on Selected Areas in Communications, Special Issue on “Femtocell Networks”, April 2012.

!

Modeling a Heterogeneous Cellular Network (HCN)

20

25

10

15

T diti l id d l0 5 10 15 20 250

5

A t l 4G ll t dTraditional grid model Completely random BSsActual 4G macrocells today

cells

Zoo

m

w/ f

emto

c

m w

/ pico

c

Zo

om

cells

too

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Effect of network geometry

SINR is one of the main performance metrics in wirelesscommunications:

SINR(y) =Pt(x0)Ah0 ‖x0 − y‖−η

N +∑

xi∈ΨI

Pt(xi )Ahi ‖xi − y‖−η

Network geometry along with propagation environment affectsSINR.

SINR impacts network performance metrics such as

outage probability, Pout = P(SINR < β)coverage probability, Pc = 1− Pout

bandwidth normalized average rate, E[ln(1 + SINR)]network capacity (or throughput), C = λ(1− Pout), subject toPout < ε, λ = no. of active links per unit area

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User association

User association, spectrum access methods, etc. affectnetwork geometry (and hence SINR) and performance ofresource allocation methodsIn a single-tier network with all BSs having the same transmitpower, a user associates to the nearest BS (for which theaverage RSS is also the highest in the downlink).

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User association

Different BSs having different transmit powers.With the strongest RSS or SINR-based association, the BSmay not necessarily be the closest one.Distance to the BS depends on relative transmit powers andpropagation conditions.Example: In first fig., r is larger than rs , butr × (Ps/Pm)1/η < rs .

rs > r (Ps/Pm)1/ƞ

r

rm>r

r

rs>r

rm > r (Pm/Ps)1/ƞ

Highest RSS Connectivity

Macro-cell User Scenario Small-cell User Scenario

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Unbalanced uplink-downlink association

In downlink, a user may associate with a macro BS, while inthe uplink, it may associate with a small cell BS.

Downlink

Uplink

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Traffic offloading and load balancing

Biasing can be used in multi-tier cellular networks to offload usersfrom one network tier to another tier.

Biasing is known as range extension in the 3GPP standard.

Instead of associating to the network entity offering the highestsignal power, a user associates to a small cell if

PsTr−ηs > Pmr

−ηm , where T ≥ 1.

i.e., if rm >(

Pm

PsT

) 1η

rs .

Without biasing, rm >(

Pm

Ps

) 1η

rs , that is, biasing will decrease the

minimum distance between a small cell user and interfering MBSs.

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Multi-tier cognitive cellular network

Each network element performs spectrum sensing to accessthe spectrum.

Cognitive spectrum access affects the locations and density ofinterferers.

re

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Challenges in HetNet modeling, analysis, and design

Traditional grid-based model fails to capture the basic HetNetcharacteristics.

New modeling/design paradigms are required.

Need design methods that account for the topological randomness

Consider universal frequency reuse (which is essential for highspectral efficiency).

Network functionalities and their optimization techniques have to berevisited and adapted to the HetNet characteristics.

Centralized control for HetNets is infeasible.

Innovative distributed network management is required.

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Stochastic geometry for modeling HetNets

Stochastic geometry is a powerful tool used to study and analyzenetworks with random topologies.

Stochastic geometry has been successfully adapted to model ad hocwireless networks from more than three decades.

Stochastic geometry has recently been used to model and analyzesingle-tier cellular networks and HetNets.

Stochastic point process is used to abstract the network model.

Stochastic geometry analysis provides statistical and spatialaverages for the performance metrics.

Stochastic geometry analysis

distribution

Physical layer characteristics

MAC layer behavior

Distribution of simultaneous active nodes

Network Capacity

Outage Probability

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Preliminaries: Stochastic Geometry and Poisson Point Process

Point process

A stochastic point process is a type of random process for whichany one realization consists of a set of isolated points either intime or geographical space, or in even more general spaces.

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Applications of point processes

Modeling and analysis of spatial/temporal data

Diverse disciplines: forestry, plant ecology, epidemiology,geography, seismology, materials science, astronomy,economics

Frequently used as models for random events in time, e.g.,arrival of customers in a queue (queueing theory), impulses ina neuron (computational neuroscience), particles in a Geigercounter, location of users in a wireless/mobile network,searches on the web

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Formulation of a point process

by observing the arrival or inter-arrival timeby counting the number of pointsby counting the number of points within a specific interval orregion

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Constructing a new point process

By transforming or changing an existing point processTransformation operations include:

mapping (scaling, translation, rotation, projection, etc. )superpositionclusteringthinningmarking

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Major point processes

Stochastic point process is used to abstract the networktopology.

Four main point processes used in the literature for modelingwireless networks:

Poisson point process (PPP)binomial point process (BPP)hard core point process (HCPP)Poisson cluster process (PCP)

PPP is the simplest and most widely used point process.

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PPP, HCPP, and PCP

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

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Poison Point Process (PPP)

PPP provides tractable results that help understanding therelationship between the performance metrics and the designparameters.

PPP can model random network with randomized channel access.

Provides tight bound for networks with planned deployment andnetworks with coordinated spectrum access

Most of the available literature assume that the nodes aredistributed according to a PPP.

Results obtained using PPP are accurate (within 1-2 dB) with thoseobtained (by measurements) for legacy cellular networks as well asHetNets.

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PPP

Let Ψ = {xi ; i = 1, 2, 3, ...} be a point process in Rd withintensity λd , then Ψ is a PPP iff

for any compact set A ⊂ Rd , the number of points in A is aPoisson random variablenumbers of points existing within disjoint sets are independent.

Number of points inside any bounded region A ∈ Rd is givenby

P{N(A) = k

}=

(λd A

)ke−λd A

k!

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PPP

Slivnyak’s theorem: the statistics seen from a PPP is independentof the test location.

Campbell’s theorem (valid for a general point process): Letf : Rd → [ 0,∞) be a function over a PP Ψ and Λ(B) is theintensity of the PP. Then the average of the sum of the function

E

[∑xi∈Ψ

f (xi )

]=

∫Rd

f (x)Λ(dx)

i.e., when the transmitting nodes form a point process Ψ and f (x)represents path-loss, the average interference seen at the origin.

Example: For a PPP with density λ, E

[ ∑xi∈Ψ

f (xi )

]= λ

∫Rd f (x)dx ,

and when f (x) = ||x ||−η (i.e., singular path-loss model), for

d = 2, E(I) = E

[ ∑xi∈Ψ

f (xi )

]= 2πλ

∫∞0

r−ηrdr = 2πλ[r2−η

2−η

]∞0

=

∞. 30/48



PPP

E[I] =∞ for a PPP with a singular path-loss model.

A consequence of the path-loss law and the property of the PPPthat nodes can be arbitrarily close

Probability generating functional (PGFL): the average of aproduct of a function over the point process

PGFL for PPP:

E

[∏xi∈Ψ

f (xi )

]= exp

{−∫Rd

(1− f (x)) Λ(dx)

}.

A PGFL is very useful to evaluate the Laplace transform of the sum∑x∈Ψ f (x).

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Poisson field of interferers and aggregate interference

Laplace transform of the pdf of interference for a PPPnetwork:

LI(s) =e−λπ

((Ps)

2η E[h

2η ΓL(1− 2

η ,Pshr−ηe )

]−r2

e E[

1−e−Pshr−ηe

])

where h can follow any distribution.

For Rayleigh fading,

LI(t) =e−πλ

((Ps)

2η Eh

[h

2η ΓL(1− 2

η ,sPhr−ηe )

]− Psr2

ePs+µr

ηe

).

For η = 4,

LI(s) =e−πλ

√Psµ arctan

(√Psµ

r2e

).

In general, the Laplace transform cannot be inverted toobtain the pdf of the interference.

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Modeling steps

1 Abstract the network into a convenient point process.

2 Identify the network geometry w.r.t. the test receiver basedon the network characteristics.

3 Identify the point process for the interference sources andderive its parameters.

4 Derive the Laplace transform (LT), moment generatingfunction (MGF) or the characteristic function (CF) of the pdfaggregate interference.

Note that MGF of I(t) = LI(−s) and CF of I(t) =LI(−jω), where j =

√−1 and ω is a real-valued parameter.

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Categorization of Performance Evaluation Techniques

Five techniques for performance evaluation

There are FIVE main techniques to overcome the problem dueto the non-existence of pdf of the aggregate interference.

1 Assume Rayleigh fading and obtain the exact SINR statistics2 Obtain tight bounds3 Generate moments/cumulants and approximate the pdf4 Plancherel-Parseval theorem5 Inversion

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Technique #1: Rayleigh fading assumption

With Rayleigh fading on the useful link, forinterference-limited networks, the cdf of SINR (i.e., outageprobability) for a receiver at a distance r from its transmitteris evaluated as FSINR(θ) = 1− LI(s)|s=cθ

FSINR(θ) = P {SINR ≤ θ}

= P{

PtAh0r−η

N + I≤ θ

}

= 1− P{h0 >

(N + I)θrη

PtA

}

= 1− E[

exp

(−

(N + I)µθrη

PtA

)]

= 1− exp

(−

Nµθrη

PtA

)E[

exp

(−Iµθrη

PtA

)]

= 1− exp (−Ncθ) LI (s)|s=cθ , where c =µrη

PtA. (1)

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Technique #1: Rayleigh fading assumption

Coverage probability, Pc = 1− FSINR(θ)= exp (−Ncθ) LI(s)|s=cθ.

With Rayleigh fading, the coverage probability in aninterference-limited network is

Pc =

∫rfR(r)LI(cθ)dr . (2)

The average transmission rate is

E[ln (1 + SINR)] =

∫ ∞0

P {ln (1 + SINR) > t} dt

=

∫ ∞0

P{

SINR >(et − 1

)}dt

=

∫ ∞0

e−Nc(et−1)LI(c(et − 1

))dt. (3)

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Technique #2: Dominant interferers by region bounds ornearest n interferers

Tight lower bound on the cdf of SINRcan be obtained by looking at thevulnerability region.

Laplace transform of theinterference distribution is notrequired.

For deterministic channel gains, thevulnerability radius is given by

rv = β1η r .

Vulnerability Circle Bx(rv)

rv

r

x

Tight lower bound on the cdf of SINR can also be obtained byconsidering the strongest n interferers.

Upper bound can be obtained by Markov inequality, Chebyshev’sinequality, Jensen’s inequality, or Chernoff bound.

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Technique #2: Dominant interferers by region bounds

For example, in CSMA networks, transmitters contend toaccess the spectrum.

Contention-based access creates protection regions for thereceivers.

Protection regions are centred around transmitters.

Vulnerability region is crescent shaped.

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Technique #2: Dominant interferers by region bounds

Divide the aggregate interference I into interferences from twodisjoint regions I1 and I2.

According to the PPP, I1 and I2 are independent, and the outageprobability is obtained as

P{S

I< θ

}= P

{I >

S

θ

}= P

{I1 + I2 >

S

θ

}= P

{I1 >

S

θ

}+ P

{I2 >

S

θ

}+ P

{I1 + I2 >

S

θ|I1 <

S

θ, I2 <

S

θ

}︸︷︷︸

=0

= P{I1 >

S

θ

}+ P

{I2 >

S

θ

}> P

{I1 >

S

θ

}= P {Ψ ∩ Bx (rv ) 6= φ}

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Technique #3: Approximation of the pdf of interference

We can resort to approximate the pdf of the aggregateinterference using the moments generated from LT, MGF orCF

There is no fixed criterion how to choose the approximate pdffor the interference.

Accuracy can only be validated via simulations.

The aggregate interference has be approximated by using theGaussian distribution, complex Gaussian distribution,truncated alpha-stable distribution, and log-normaldistribution.

Moments or cumulants are generated using the LT as follows:

E[Inagg] = (−1)ndn

dsnLIagg(s)

∣∣∣∣s=0

(4)

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Technique #4: Plancherel-Parseval theorem (Fourierintegration technique)

Plancherel-Parseval theorem states that if f1(t) and f2(t) aresquare integrable complex functions, then

∫Rf1(t)f ∗2 (t)dt =

∫RF1(ω)F∗2 (ω)dω

The Fourier transform of a function is equivalent to the CF ofthat function, which can be obtained from its Laplacetransform.

Plancherel-Parseval theorem precludes the need of invertingthe Laplace transform of pdf of interference (i.e., Laplacetransform itself can be used for performance evaluation).

Results for general fading environment can be obtained.

The integrals are quite involved due to the complex nature ofthe characteristic functions.

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Technique #4: Example

Suppose we want to calculate the coverage probability

P{S

I> θ

}= P

{I < S

θ

}=

∫y

1{y< Sθ}fI(y)dy

The indicator function has the Fourier transform

1{y<θ}FT

=⇒ 1− e−2πiωθ

2πiω, and (5)

fI(y)FT

=⇒ F(ω)

Fourier transform can be directly obtained from the Laplacetransform, i.e., FI(ω) = LI(−2πiω)

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Technique #4: Example

Then using Plancherel-Parseval theorem, we have

P{S

I< θ

}=

∫y

1{y< Sθ}fI(y)dy

=

∫ω

LI(−2πiω)1− e−

2πiωSθ

2πi Sθdω

If S is random, then the unconditional coverage probability isobtained as

P{S

I< θ

}=

∫s

fS(s)

∫ω

LI(−2πiω)1− e−

2πiωsθ

2πi sθdωds

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Technique #5: Inversion

The LT, CF, or MGF is inverted to obtain the pdf of theinterference.

Due to the complex nature of the expressions for LT, CF, orMGF, generally we are unable to find the pdf in closed form.

This technique is only useful for very special cases of the PPP,where the expressions for LT, CF, or MGF are invertible ormatch the LT, CF, or MGF of a known distribution.

Otherwise, inversion is done numerically.

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Summary

Stochastic geometry modeling provides tractable yet accurateexpressions for several important performance metrics in terms ofthe design parameters.

Generally, the interference cannot be characterized via its pdf or cdf.

However, the LT (or CF, or MGF) of the pdf of interference can beobtained for any fading scenarios.

The cdf of SIR or the lower/upper bounds on the cdf of SIR can beobtained for any fading scenarios (in both useful and interferencelinks).

Technique #1 and technique #2 are the most popular performanceevaluation techniques due to their simplicity and tractability.

Technique #4 provides a potential to obtain exact general resultsvia stochastic geometry modeling, but at the expense of reducedtractability.

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Summary

Stochastic geometry is an elegant mathematical technique to modelcellular networks.

Under certain assumptions stochastic geometry gives simpleclosed-form expressions for the performance metrics.

PPP gives accurate lower bound for the coverage probability andachievable data rate.

The baseline models can be extended and capture more realisticcellular network characteristics.

The different techniques in the literature can be exploited forrelaxing some of the simplifying assumptions (e.g., Rayleigh fadingassumption).

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Future research directions

More accurate/general point processes

New performance metrics

More practical system model

cognitioncooperative multipoint transmission (COMP)MIMOmobilitymultiple channelsdifferent channel allocation strategies,power control

Uplink modeling

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Thank you!

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Modeling, Analysis, and Design of Multi-tier and Cognitive Cellular Wireless Networks - Prof Ekram...

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